We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of spatially localized vibrational modes, serving as a model of Dynamic Nuclear Polarization. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect, as manifested by the hole-burning shape of the electron paramagnetic resonance spectrum. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4 - 5 Kelvin.
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